Chapter 10.
Generating Prisms
This chapter describes the automatic and manual procedure for creating prisms in TGrid.
It also discusses the solution to some common problems that you may face while creating
prisms.
This chapter comprises the following sections:
• Section 10.1: Overview
• Section 10.2: Procedure for Generating Prisms
• Section 10.3: Prism Meshing Options
• Section 10.4: Zones Created During Prism Generation
• Section 10.5: How TGrid Builds Prisms
• Section 10.6: Using Adjacent Zones as the Sides of Prisms
• Section 10.7: Direction Vectors
• Section 10.8: Offset Distances
• Section 10.9: Improving Prism Quality
• Section 10.10: The Prisms Panel
• Section 10.11: Text Interface for Generating Prisms
• Section 10.12: Prism Meshing Problems
10.1
Overview
In TGrid, you can create 3D prism cells starting from either quadrilateral or triangular
boundary faces (or both). The 2D prism cells (quadrilateral) can be created starting
from linear faces. Prisms can be used to resolve a boundary layer region of a triangular
or tetrahedral mesh. They can be used to extend some portion of a domain for which
the volume mesh already exists (e.g., increase the length of an inlet pipe), or to create a
volume mesh by extrusion. To create prisms, you need to specify the boundary zone(s)
from which the prisms will be built, their heights, and the direction in which you want
to build them.
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Generating Prisms
TGrid also allows you grow prisms on dangling walls. You can also specify different
growth methods on adjacent walls in the domain. TGrid can automatically detect the
collision between the prisms layers and avoid the collision by adjusting the height of the
colliding prism layers.
Figure 10.1.1 shows the types of prisms that TGrid can generate.
Figure 10.1.1: Prism Shapes that TGrid Creates
Instructions for building prisms are provided in Section 10.2: Procedure for Generating
Prisms. Details about how TGrid uses your inputs to generate the prisms are provided
in Section 10.5: How TGrid Builds Prisms. Problems related to prism generation are
discussed in Section 10.12: Prism Meshing Problems.
10.2
Procedure for Generating Prisms
The procedure for creating prisms from boundary zones is as follows:
1. Check the boundary mesh to ensure that free nodes or faces with high skewness do
not exist. See Sections 7.1 and 14.2 for details.
2. Select the boundary zone(s) from which you want to grow prisms in the Boundary
Zones selection list in the Prisms panel.
Mesh −→Prisms...
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If you read in a mesh file created in a previous version of TGrid, it is
recommended that you reset all the prism parameters using the command
/mesh/prism/reset-parameters before proceeding with setting the prism
parameters.
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10.2 Procedure for Generating Prisms
3. Specify prism growth parameters in the Growth tab.
(a) Select the appropriate Offset Method and Growth Method for growing prisms.
See Sections 10.8 and 10.10 for details.
(b) Define the height of the first prism layer (First Height/First Aspect Ratio).
(c) Set the growth method related parameter (Slope, Rate, or Exponent, as applicable) and the Number of Layers.
(d) Specify options for proximity detection and ignoring prisms in regions of proximity and invalid normals in the Prisms Growth Options panel (opened using
the Growth Options... button), if required. Refer to Section 10.3: Prism Meshing Options for details.
(e) Click the Plot or Print button to preview the height distribution.
For information on setting different growth parameters for different zones, see
Section 10.3.1: Growing Prisms Simultaneously from Multiple Zones.
4. Specify the direction for prism growth (see Section 10.7: Direction Vectors).
(a) Enable the display of normals in the Attributes section of the Display Grid panel
and click Apply.
Display −→Grid...
(b) Click the Direction tab in the Prisms panel to view the direction parameters.
(c) Click Draw and check if the normal vectors for each zone are pointing in the
direction that you want to build the prisms.
• If the vectors for the faces on each zone do not point in the same direction
(i.e., if some point on one side of the zone and others point on the other
side), click the Orient Normals button to reorient them.
• If the vectors point in the wrong direction, click the Flip Normals button
to reverse the direction.
(d) Display the zone(s) to verify that the normals now point in the correct direction.
(e) Specify the method for determining the direction of the prisms:
• Select Normal in the Method list to compute normal direction vectors.
This method takes into account the change in direction required for a
curved region. Specify the values for the maximum angle change.
• Select Uniform in the Method list to use a constant, uniform direction for
flat prism regions. Specify the appropriate direction vector.
5. Set the parameters for prism improvement and prism projection available in the
Improve and Project tabs, respectively, as required.
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Generating Prisms
6. Click Apply to save your settings.
7. Save the mesh.
File −→ Write −→Mesh...
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It is a good practice to save the mesh at this point. If you are dissatisfied
with the prisms generated, you can read in this mesh and modify the prism
parameters to regenerate the prisms.
8. Click Create to generate the prisms.
Refer to Section 10.12: Prism Meshing Problems for suggestions on solving problems
occurring during prism generation.
9. Check the maximum face skewness value reported in the TGrid console when the
final prism layer is created, to ensure that the value is acceptable.
This is only for 3D and is especially important if you are going to generate tetrahedral or pyramidal cells using this new boundary zone.
The new zone should not have highly skewed triangles or quadrilaterals. For more
information about the quality of quadrilateral faces used for creating pyramids, see
Section 9.3.1: Creating Pyramids.
If the reported maximum skewness is too high, read the mesh file you saved after
setting the prism parameters and try again with different parameters. For details,
see Section 10.12: Prism Meshing Problems.
10. A number of new zones are created when the prism generation is complete (see
Section 10.4: Zones Created During Prism Generation). If the prism-cap or prismside face zones are not supposed to be walls (e.g., if they are supposed to be simple
interior zones), change them to the appropriate boundary type.
Boundary −→Manage...
For most cases, performing these steps will result in an acceptable mesh of prismatic cells,
but for some complex geometries, you may have to modify the procedure. If you are not
satisfied with the prisms generated by TGrid, you can read in the mesh you saved before
generating prisms and modify the prism parameters. Refer to Sections 10.5—10.12 for
details on modifying the prism generation parameters to create a better mesh.
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10.3 Prism Meshing Options
10.3
Prism Meshing Options
This section describes various the options available in TGrid while creating a prism mesh
for the domain.
10.3.1
Growing Prisms Simultaneously from Multiple Zones
You can select multiple face zones for simultaneously growing prism layers. If the face
zones are connected, the prisms grown will also be connected. A single zone of prism cells
and a single zone of cap faces will be created for each set of simultaneously grown layers.
To retain the individual prism cell zones and cap face zones, enable Grow Individually in
the Prisms Growth Options panel (opened by clicking the Growth Options... button).
TGrid allows you to grow prisms from multiple zones with the same or different growth
parameters.
• To use the same growth parameters for all zones, follow the steps in Section 10.2: Procedure for Generating Prisms. In this case, the same number of layers are grown
from all zones, and all other parameters (growth method, offset method, direction
method, etc.) will remain the same.
• To use different growth parameters for different zones, apply different growth methods, offset methods, first height, and other growth parameters (as required for the
growth method selected) individually for each zone and click the Apply button in
the Zone Specific Growth group box in the Prisms panel.
If you specify different growth parameters for different zones, all other parameters
(direction method, offset method, etc.) can be set separately for each zone. In this
case, the offset height of each node that is shared by multiple zones will be the
average of the heights applied on the separate zones.
This produces a continuous transition between the zones (Figure 10.3.1). Offset
smoothing (see Section 10.8: Offset Smoothing) is recommended in these cases to
avoid sharp height changes at such edges.
To assign different growth controls and different offset types to different face zones,
replace steps 2 and 3 in Section 10.2: Procedure for Generating Prisms with the following
steps:
1. Select the zone(s) for which you want to specify a set of growth parameters in the
Boundary Zones list in the Prisms panel.
2. Set the appropriate Offset Method, Growth Method, First Height, and the related
growth parameters (as required) in the Growth tab.
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Generating Prisms
Figure 10.3.1: Different Growth Methods on Adjacent Zones
3. Specify parameters for proximity/collision detection in the Prisms Growth Options
panel (see Section 10.3.3: Detecting Proximity and Collision for details).
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By default, TGrid generates a single zone of prism cells and cap faces for the
simultaneously grown prism layers. If you want to retain individual prism
cell zones and cap faces, enable Grow Individually in the General Options
group box in the Prisms Growth Options panel.
4. Click Apply in the Prisms panel.
5. Repeat this procedure for other zones for which you want to apply different growth
controls.
6. Click Create.
!
10.3.2
Before you click the Create button, ensure that all the zones for which you
want to grow prisms are selected in the Boundary Zones list.
Growing Prisms on a Two-Sided Wall
Two-sided walls may be present in some geometries. To grow prisms on both sides of a
two-sided wall (e.g., growing prisms on dangling walls), do the following:
1. Select the two-sided wall on which you want to grow prisms from the Boundary
Zones selection list.
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10.3 Prism Meshing Options
2. Specify the prism growth parameters as required.
3. Enable Grow on Two Sided Wall in the Growth tab of the Prisms panel.
4. Click Create. See Figure 10.3.2 for details.
Figure 10.3.2: Prism Growth on a Dangling Wall
10.3.3
Detecting Proximity and Collision
If the zones on which you want to grow prisms are very close to each other, the prism
layers from zones may intersect or collide with each other. This results in bad quality of
prism layers.
For example, in Figure 10.3.3, the prism layers grown from proximal surfaces intersect
each other. The Allow Shrinkage option in TGrid allows you to avoid the intersection of
prism layers by adjusting the height of the prism layers in closely placed zones. Figure 10.3.4 shows the use of this option to avoid intersection of the prism layers by adjusting the prism layer height.
A value of n for Gap Factor implies that a gap equal to n times the maximum base edge
length at the node in question will be maintained. Hence, a value of 1 implies that the
gap maintained is equal to the maximum base edge length at the node considered.
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Offset heights are scaled only in the regions where the intersection of prism
layers takes place. For the remaining regions, the prisms are created according to the specified parameters.
You can also ignore prisms regions of close proximity during prism generation. The area
of proximity will be determined based on the shrink factor specified. Prism layers will
be grown from the remaining geometry according to the specified parameters.
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Generating Prisms
Figure 10.3.3: Collision of Prism Layers
Figure 10.3.4: Prism Layers Shrunk to Avoid Collision
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10.3 Prism Meshing Options
Figure 10.3.5 shows a portion of the geometry where the region of proximity in a sharp
corner has been ignored while creating prisms.
Figure 10.3.5: Ignoring Areas of Proximity
For automatic adjustment of intersecting/colliding prism layers while growing prisms, do
the following:
1. Specify the prism growth parameters.
2. Click the Growth Options... button in the Growth tab to open the Prisms Growth
Options panel (see Section 10.10.1: The Prisms Growth Options Panel).
3. Enable the appropriate options in the General Options group box.
4. Specify the parameters required for the proximity calculation and controlling the
prism layer height.
Enable Allow Shrinkage to allow shrinkage of prism layers in areas of proximity.
This option is enabled by default.
Enable Keep First Layer Offsets, if required.
This option allows you to keep the original first offset height and scale the
offset heights for the remaining layers in case of intersecting prism layers.
Specify an appropriate value for Gap Factor.
Enable Allow Ignore to ignore the prism growth parameters in areas of proximity.
Enter an appropriate value for Max Aspect Ratio or Max Shrink Factor as required.
Click Apply and close the Prism Growth Options panel.
5. Click Create in the Prisms panel.
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Generating Prisms
10.3.4
Ignoring Invalid Normals
Some geometries may contain regions where the normals considered while growing prisms
may be invalid. The normal at a particular node may be nearly tangential to the surrounding faces in the geometry and as a result, the prism generation may fail. For such
cases, you can choose to ignore regions of the geometry where invalid normals exist, during prism generation. Prism layers will be grown from the remaining geometry according
to the specified parameters.
Figure 10.3.6 shows a portion of the geometry where the normal at the highlighted node
will be nearly tangential to some of the surrounding faces. You can see that the region
around this node has been ignored while creating prisms.
Figure 10.3.6: Ignoring Invalid Normals
You can ignore regions based on normals while creating prisms as follows:
1. Specify the prism growth parameters.
2. Select the Boundary Zone containing the invalid normal and click the Growth Options... button to open the Prisms Growth Options panel.
(a) Enable Ignore Invalid Normals in the General Options group box.
(b) Click Apply and close the Prism Growth Options panel.
3. Grow prisms as required.
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10.3 Prism Meshing Options
10.3.5
Preserving Orthogonality
In some cases, it may be important for the prismatic mesh to be orthogonal near the
original boundary. For such cases, there are two ways to preserve orthogonality:
• Decrease the value specified for the Max. Angle Change in the Direction tab of the
Prisms panel to a lower value to limit the change in normal direction in each prism
layer.
This parameter is set to 45 degrees by default. This means the normal direction
at a node can change up to 45 degrees during normal, edge, and node smoothing.
For example, if you reduce this parameter to 10 degrees, the change in normal
direction will be more gradual, and the mesh near the original boundary will be
nearly orthogonal.
• Specify an explicit number for Orthogonal Layers in the Direction tab of the Prisms
panel.
When you specify orthogonal layers, you should decrease the Max Angle Change
to approximately 10 degrees. This will prevent sudden sharp changes in normal
direction at the first non-orthogonal layer.
For a non-orthogonal layer, TGrid will perform edge swapping normal, edge, or node
smoothing so that the layer is orthogonal to the original boundary. For example,
if you specify 5 orthogonal layers, no smoothing will be performed on the first 5
layers, resulting in direction vectors that are normal to the original surface mesh
faces. Full smoothing is used on the sixth and subsequent layers.
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If you are preserving orthogonality near the original boundary, make sure
that the prism layers do not grow too quickly. Use small layer heights,
relative to the sizes of the faces on the original boundary. If prism layers
grow quickly, the nearly-orthogonal direction vectors are likely to cross at
sharp concave corners, causing the prism generation to fail. TGrid will
stop the prism layer generation at this point. See Section 10.7: Normal
Smoothing.
Preserving orthogonality can affect skewness and lead to left-handed faces and/or negative volumes. See Section 10.12: Negative Volumes/Left-Handed Faces/High Skewness
for details.
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Generating Prisms
10.4
Zones Created During Prism Generation
When TGrid generates prisms, several new cell and face zones are created. You can
identify the new zones by their default names.
• The cell zone containing the prisms will be named prism-cells-n.
• The face zone created at the end of the last prism layer will be named prism-cap-n.
• If the prism layers are bounded by one or more existing triangular face zones, each
of these will be retriangulated so that the faces of the zone that are adjacent to
the prisms will become quadrilateral faces, while the rest of the faces in the zone
remain triangles.
If an original triangular face zone is called symmetry the portion of it that still contains triangles will be retained as symmetry, while the portion containing quadrilateral faces will be named symmetry-quad:n.
• Any faces that were not projected to adjacent zones (see Section 10.6: Using Adjacent Zones as the Sides of Prisms) are collected into a zone named prism-side-n.
• For a zone wall-n, the zone created by ignoring prism growth in the region of
proximity will be named as wall-n:ignore, where, n is the zone number assigned
by TGrid.
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TGrid will merge all the ignored threads related to a base thread into a
single thread by default. You can however change this using the command
/mesh/prism/controls/merge-ignored-threads? which will generate
more than one thread per base thread.
To merge one or more prism cell zones with other cell zones (and merge the corresponding
face zones), use the Merge option in the Manage Cell Zones panel (see Section 13.9.3: The
Manage Cell Zones Panel).
By default, the prism-cap-n zones will be wall zones. If you do not want to include
these walls in the model, change them to interior zones (or any other type) using the
Manage Face Zones panel (see Section 7.13.1: The Manage Face Zones Panel).
10.5
How TGrid Builds Prisms
TGrid follows the following steps to build the prism and to create a high-quality mesh.
1. Boundary mesh analysis:
Analyze the initial surface mesh to determine if any adjacent zones should be
projected to and retriangulated (if triangular), or if their faces should be used
as the sides of new prism cells (if quadrilateral).
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10.5 How TGrid Builds Prisms
For details on how TGrid determines whether to use existing boundary zones or not
see Section 10.6: Using Adjacent Zones as the Sides of Prisms
2. Prism layer growth.
Grow layers of prisms one by one, based on the layer height specification. This is
a multi-step procedure, and hence you can modify or skip some of the steps:
(a) Determine the initial direction vectors so that TGrid will know the direction
in which to build the prisms. Several advancement direction methods are
available, as discussed in Section 10.7: Direction Vectors.
(b) Smooth the initial direction vectors. See Section 10.7: Normal Smoothing for
details.
(c) Determine the initial offset distances so that TGrid will know how far from the
corresponding nodes on the previous layer to place the new nodes that define
the prisms. See Section 10.8: Offset Distances for details.
(d) Smooth the offset distances are smoothed to eliminate spikes and dips in the
new prism layer. See Section 10.8: Offset Smoothing for details.
(e) Project new nodes along the outer edges of the prism layer to adjacent zones,
based on the analysis in step 1.
(f) Create prism faces and cells using the new nodes. The new faces at the top of
the prism layer are referred to as cap faces.
(g) The new cap faces of skewness value greater than the specified threshold are
improved by edge swapping or edge node smoothing. See Section 10.9.1: Edge
Swapping and Smoothing for details.
(h) Apply global smoothing across the new surface. This is also skewness-driven,
but is based on the nodes not the faces. See Section 10.9.2: Node Smoothing
for details.
(i) Check the quality of all new cells and faces.
(j) If quality problems are detected, prism layer creation is stopped. If more layers
are to be grown, the process is repeated starting from substep (a).
3. Zone clean up: After all the prism layers have been grown, the new faces along the
outer sides of the layers are moved to zones of the same types as the zones to which
their nodes are projected. Unprojected faces are collected in a single prism-side
zone.
4. Retriangulation: Adjacent triangular zones that have been projected to are automatically retriangulated. Triangles that are overlapped by new quadrilateral faces
from the prism layers are removed. Most of the original nodes are used in the new
triangulation. The result is a conformal interface between the sides of the prism
layers and the adjacent triangular zones. An analogous procedure is used in 2D.
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Generating Prisms
10.6
Using Adjacent Zones as the Sides of Prisms
For each zone adjacent to the zone(s) from which you grow prisms, TGrid will check the
angle between the prism growth direction and the adjacent zone. Depending on the size
of this angle, TGrid will decide whether to use the adjacent zone for the prism sides, or
create a new zone.
Using Adjacent Quadrilateral Face Zones
If an adjacent zone has quadrilateral faces, it will be used without modification as the
prism-side boundary, and it satisfies the following requirements:
• It must share nodes with the boundary zone from which you are building the prisms
i.e., there must be no free nodes (see Section 7.1.1: Free and Isolated Nodes) where
the zones touch.
• The angle between the adjacent zone and the prism growth direction must be less
than the specified threshold, Max. Adjacent Zone Angle in the Project tab of the
Prisms panel. The default threshold value is 45 degrees.
For example, if you are growing prisms from the bottom surface in Figure 10.6.1 using
the default maximum adjacent zone angle of 45 degrees, the zone on the left will be
excluded, but the zone on the right will be used as it is. A new zone will be created for
the left sides of the prisms.
Figure 10.6.1: Effect of Adjacent Zone Angle
To fill in the gap on the left side of Figure 10.6.1, (in 2D) create a domain enclosing the
gap and generate triangular cells, or (in 3D) create pyramids using the prism side faces,
create a domain, and generate tetrahedral cells.
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10.6 Using Adjacent Zones as the Sides of Prisms
Projecting to Adjacent Triangular Face Zones
If an adjacent zone has triangular faces, TGrid will perform two additional steps to
incorporate the zone into the prism layers: projection and retriangulation. TGrid will
project the outer nodes of the prisms onto the triangular faces of the adjacent zone,
provided it satisfies the following requirements:
• It must share nodes with the boundary zone from which you are building the prisms.
That is, there must be no free nodes (see Section 7.1.1: Free and Isolated Nodes)
where the zones touch.
• The angle between the adjacent zone and the prism growth direction must be less
than the specified threshold, Max. Adjacent Zone Angle (in the Project section of
the Prisms panel). The default threshold value is 45 degrees.
In Figure 10.6.1, the zone on the right will be projected to and retriangulated, while the
zone on the left will be excluded.
Retriangulation
As shown in Figure 10.1.1, the sides of the prism will always be quadrilateral faces,
regardless of the type of face from which a 3D prism is built (triangular or quadrilateral).
If the prism-side nodes are projected to an adjacent triangular boundary face zone:
1. The prism-side faces on the shared boundary will be overlaid on the triangular faces
of the existing boundary zone.
2. TGrid will retriangulate the triangular boundary zone so that the triangular portion
of the zone ends at the border of the portion now filled with quadrilateral faces.
This is done to obtain a conformal mesh where all the nodes match up at face
edges.
3. The triangles that were overlapping the quadrilateral prism-side faces will be deleted.
Figure 10.6.2 shows the initial boundary mesh for a car and the symmetry boundary
beside it. If the prisms are generated from the car body without retriangulation of
the triangular symmetry boundary, the resulting boundary mesh will be as shown in
Figure 10.6.3. With retriangulation, the boundary mesh will appear as in Figure 10.6.4.
Though it is possible to disable retriangulation (by disabling the Retriangulate Adjacent
Zones option in the Project tab of the Prisms panel), it is not always recommended. Expert
users experimenting with different settings may temporarily turn off retriangulation.
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Generating Prisms
Figure 10.6.2: Symmetry Zone and Car Wall Before Prism Generation
Figure 10.6.3: Symmetry Zone and Car Wall After Prism GenerationWithout
Retriangulation
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10.7 Direction Vectors
Figure 10.6.4: Symmetry Zone and Car Wall After Prism Generation and
Retriangulation
10.7
Direction Vectors
As TGrid builds each layer of prisms, it needs to know which direction to build in. There
are two methods available for determining the direction vectors:
• Extrusion Method: For creating straight-sided prism regions without any curvature, you can specify a uniform direction vector for all prism layers. Select Uniform
in the Method list in the Direction tab of the Prisms panel.
Figure 10.7.1: Uniform Direction Vector for a Straight-Sided Prism Region
Specify the uniform direction vector or click Compute in the Vector group box.
TGrid will use this constant vector for all prism layers, instead of computing a new
direction for each layer (see Figure 10.7.1).
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Generating Prisms
• Normal Method: For regions with curvature, TGrid determines the appropriate
normal direction vector at each node, since it may be different for each node and
each layer, see Figure 10.7.2. Select Normal in the Method group box in the Direct
tab of the Prisms panel.
Figure 10.7.2: Normal Direction Vectors for a Curved Prism Region
Normal Smoothing
The normal direction vectors obtained using the methods described in Section 10.7: Direction Vectors are smoothed so that there is a gradual change in direction from one node
to the next. This will reduce the chance of direction vector intersection, which causes
the prism generation to fail. This step is not necessary when a uniform direction vector
is used, since there is no change in direction from one node to the next.
Figure 10.7.3 shows normal direction vectors in the vicinity of a sharp (90 degree) corner.
Figure 10.7.3: Normal Direction Vectors Before Smoothing
The direction vector is at an angle of 45 degree at the corner, while elsewhere it is 0
or 90 degrees. These direction vectors will intersect and prisms cannot be generated.
Figure 10.7.4 shows the normal direction vectors near the corner after they have been
smoothed. After smoothing, the normal direction changes more gradually from node to
node.
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10.8 Offset Distances
Figure 10.7.4: Normal Direction Vectors After Smoothing
It is possible to create very thin prism layers using the direction vectors shown in Figure 10.7.3, as long as the last layer lies below the point where the vectors cross.
10.8
Offset Distances
The offset distance for a given node is the distance between adjacent layers at that node.
This distance is based on the prism layer height computed from the specified prism
growth parameters. The new node for a prism layer is placed at this distance along the
direction vector.
There are four methods available for determining the offset distances:
• Uniform Offset Distance Method: In this method, every new node (child) is
initially the same distance away from its parent node (i.e., the corresponding node
on the previous layer, from which the direction vector is pointing).
Figure 10.8.1: Uniform Offset Distance Method
Uniform distances are fine for planar surface meshes, but they result in crevices at
sharp corners, for example, the 90 degree corner in Figure 10.8.1. The direction
vector at the corner node will be at an angle of 45 degrees, while the vectors at
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Generating Prisms
the adjacent nodes will be slightly more orthogonal to their faces. For uniform
distances, this places the nodes for the first layer as shown in Figure 10.8.1.
The dashed line connecting the new nodes begins to pinch inward at the corner.
The distances between parent and child nodes are still all the same, but the angles of
the direction vectors introduce this pinching effect. Without some sort of correction
such crevices can eventually collapse.
• Minimum Height Offset Distance Method: In this method, child nodes are
guaranteed to be at least as far from their parent nodes as the distance computed
for the current layer from the growth inputs. TGrid will also try to retain the shape
of the original boundary.
Figure 10.8.2: Minimum-Height Offset Distance Method
For a perfect 90 degree corner, this results in a perfect 90 degree corner for the next
layer (see Figure 10.8.2). Thus, in this method the shape is better preserved if no
additional smoothing is applied.
The minimum height method have some limitations. If the angle of the direction
vector at the corner is not 45 degrees (i.e., if it does not exactly bisect the angle
between the faces), the minimum-height method can increase skewness.
• Aspect Ratio Method: This method allows you to control the aspect ratio of
the prism cells that are extruded from the base boundary zone. The aspect ratio
is defined as the ratio of the prism base length to the prism layer height. The
various growth methods (constant, linear, geometric, and exponential) can be used
to specify the aspect ratio of the first layer.
When a non-constant growth method is used, the aspect ratio for subsequent layers
will change accordingly. The heights of the prism cells will vary according to the
local face sizes in the surface mesh, providing a convenient way to automatically
vary prism heights across a zone.
• Last Ratio Method: This method also allows you to control the aspect ratio
of the prism cells that are extruded from the base boundary zone. You can specify First Height for the first prism layer. If you select this method, the various
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10.8 Offset Distances
growth methods will not be accessible. The last aspect ratio method is explained
in Figure 10.8.3.
Figure 10.8.3: Last Ratio Method
Local base mesh size is used to find out the offset height for the last layer. For
example, if you specify 80 as the Last Percent value the offset height of the last layer
will be 0.8 times the local base mesh size. Local growth rate is used to calculate
the other intermediate offset heights exponentially.
Offset Smoothing
The purpose of offset smoothing is to eliminate spikes and dips in the new surface layer.
Smoothing is applied iteratively. Figure 10.8.4 shows how the nodes are moved during
offset smoothing.
Figure 10.8.4: Effect of Offset Smoothing
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Generating Prisms
10.9
Improving Prism Quality
TGrid performs the following to improve the skewness of prism faces:
• Edge swapping and smoothing (Section 10.9.1: Edge Swapping and Smoothing)
• Node smoothing (Section 10.9.2: Node Smoothing)
10.9.1
Edge Swapping and Smoothing
After the new triangular cap faces are created for the new layer, the skewness is compared
with the specified skewness threshold (Skewness in the Swapping and Smoothing group
box in the Improve tab of the Prisms panel). If the skewness of a face is too high, TGrid
performs the following improvement procedure:
1. Swap the longest edges of highly skewed faces.
When edge swapping occurs on a cap face, swapping propagates downward. Swapping must be performed on the corresponding faces on all prism layers, including
the face on the original boundary mesh, so that the grid lines within the prism
layers do not cross.
Swapping is not performed if it will significantly alter the geometry defined by the
original boundary mesh.
2. If swapping is not performed, TGrid will try to improve the skewness by smoothing
the nodes of the skewed faces using one of the following operations.
• If the sharpest angle at the node (i.e., the most acute angle between adjacent
faces that use the node) is nearly 180 degrees, TGrid will perform smoothing
(as described in Section 10.9.2: Node Smoothing) to move the nodes.
• If the sharpest angle is far from 180 degrees, TGrid will limit the smoothing
so that the nodes are only allowed to move along the face’s longest edge. This
method will prevent the collapse of sharp corners in the mesh.
Smoothing does not propagate downward, it is performed only on the skewed
cap faces themselves.
This edge swapping/smoothing procedure is not performed on quadrilateral cap faces.
10.9.2
Node Smoothing
If the edge swapping and smoothing are not sufficient to reduce the skewness of some
faces, include an additional smoothing operation. In this method, if any of the faces
surrounding a new node have a skewness greater than the specified threshold, the node
is smoothed.
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10.9 Improving Prism Quality
Instead of moving only the node, this method will also move the surrounding nodes to
make space for the node to move.
Figure 10.9.1: Node Smoothing in Rings
The surrounding nodes are grouped and smoothed in rings (see Figure 10.9.1). The
nodes on the outermost ring are smoothed first, etc., until the target node (on ring zero)
is finally smoothed.
This type of smoothing is helpful in concave areas where the advancing layers continually
decrease the available surface area, causing squashing of triangular faces. By smoothing
outer rings of nodes first, more space is provided for the nodes that need to be moved
in order to reduce the skewness. Thus, this method performs regional smoothing around
faces of high skewness. The node smoothing procedure can be performed on both tri and
quad faces.
10.9.3
Improving Warp
Improving warp in prisms is a postprocessing step which is carried out after all the
required prism layers are created. TGrid allows you to improve the warp in the generated
prism faces by moving the nodes of the face to make it planer.
When the Improve option is enabled in the Warp group box in the Improve tab of the
Prisms panel (see Section 10.10: The Prisms Panel), TGrid identifies the prism layer(s)
having faces with warp ≥ 0.5. The nodes on the identified faces are moved and the new
location of the node is updated only when:
1. The overall maximum warp of the faces connected to the node has decreased.
2. The overall maximum skewness of the cells connected to the node has decreased or
remained the same.
This is useful in regions having complex sharp corners, where the nodes of a prism cell
may have drastic normal change.
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Generating Prisms
10.10 The Prisms Panel
The Prisms panel allows you to specify parameters needed for prism cell creation, and
then create the prisms. When you press any of the tab buttons along the top of the panel,
the panel contents change to show the related controls. The controls for all inactive tabs
are hidden.
The Prisms panel consists of a series of tabbed frames, within the main panel, listed
horizontally across the top of the panel. Each frame has a name and a set of related
controls.
Mesh −→Prisms...
Controls
Boundary Zones contains a selection list of all of the boundary zones in your mesh.
You will select the zone(s) from which you want the prisms to be built.
Boundary Zone Groups contains a list of boundary zone types and user-defined groups.
If you select a boundary type (or group) from this list (e.g., inlet), all boundary
zones of that type (or group) will be selected in the Boundary Zones list. This
shortcut allows you to easily select all boundary zones of a certain type without
having to select each zone individually. You can select multiple boundary types in
the Boundary Zone Groups list to select all zones of several different types (e.g., inlet
and outlet).
You can also select tri or quad in this list to select all triangular or quadrilateral
boundary zones.
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10.10 The Prisms Panel
Growth displays the controls for computing the height of each layer of prisms. This is
the default tab of the Prisms panel.
Offset Method contains a drop-down list of the methods available for computing
the offset distance. See Section 10.8: Offset Distances.
uniform specifies the uniform offset method.
aspect-ratio specifies the aspect-ratio offset method.
last-ratio specifies the last-ratio offset method.
minimum-height specifies the minimum-height offset method.
Growth Method contains a drop-down list of the methods available for computing
the prism height. Figure 10.10.1 shows layer heights for all four methods, using
a first height of 1 and a slope/rate/exponent of 1.2.
Figure 10.10.1: Layer Heights Computed Using the Four Growth Methods
constant enables the specification of a constant height for all prism layers.
When this method is selected, you will need to specify the First Height
and the Number of Layers. The height of all prisms will be the First Height
(h1 ).
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Generating Prisms
linear enables the specification of a variable height that decreases or increases linearly for each layer of prisms:
hn = h1 + s(n − 1)
(10.10-1)
When this method is selected, you will need to specify the First Height
(h1 ), the Number of Layers, and the Slope (s).
geometric enables the specification of a variable height that decreases or
increases geometrically for each layer of prisms:
hn = rn−1 h1
(10.10-2)
When this method is selected, you will need to specify the First Height
(h1 ), the Number of Layers, and the Rate (r).
exponential enables the specification of a variable height that decreases or
increases exponentially for each layer of prisms:
hn = h1 e(n−1)p
(10.10-3)
When this method is selected, you will need to specify the First Height
(h1 ), the Number of Layers, and the Exponent (p).
First Height specifies the height of the first prism layer (h1 ). The computed
heights of subsequent prism layers will be based on this height, depending on
the Growth Method selected.
Number of Layers sets the total number of prism layers to be created.
Total Height reports the total height of the prisms to be grown. You can use
this information to check if the specified prism heights will yield a mesh of the
required height.
If you want to see the updated Total Height, press the <Enter> key after
entering a new value for the other growth parameters. If you do not press
<Enter> after entering the value, the Total Height reported will not reflect the
changed value.
First Aspect Ratio specifies the first aspect ratio to be used when the aspect-ratio
offset method is selected.
Last Aspect Ratio reports the last aspect ratio based on the specified first aspect
ratio for the aspect-ratio offset method.
Last Percent specifies the percentage to be used along with the First Height when
the last-ratio offset method is selected.
Slope sets the slope (s) of the linear function used to compute the heights of the
prism layers when the linear growth method is selected.
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10.10 The Prisms Panel
Rate sets the rate of growth (r) of the geometric function used to compute the
heights of the prism layers when the geometric growth method is selected.
Exponent sets the exponent (p) for the exponential function used to compute the
heights of the prism layers when the exponential growth method is selected.
Growth Options... opens the Prisms Growth Options panel (see Section 10.10.1: The
Prisms Growth Options Panel).
Edge Size Limits displays (in an Information dialog box and in the console) the
minimum, maximum, and average edge lengths for all selected Boundary Zones.
The First Height should usually be smaller than the minimum length reported.
Zone Specific Growth allows you to simultaneously grow prisms from multiple
zones using different growth parameters.
By default, this option will be enabled if you read in a mesh for which separate
growths were specified for different zones and then subsequently saved. It will
be disabled if you read in a mesh that does not have saved prism parameters.
You need not use any of these controls if you are building prisms from just one
zone, building them from multiple zones using the same growth parameters,
or growing layers for multiple zones at different times.
Grow on Two Sided Wall allows you to grow prisms on both sides of a two
sided wall.
Apply applies the specified growth parameters to the selected Boundary
Zones.
Note: When setting prism parameters for use with the Auto Mesh
option, it is necessary to apply the prism growth parameters on specific zones for TGrid to retain the growth parameters in memory.
The Prisms option in the Auto Mesh panel will be visible only after
applying zone-specific growth (by clicking Apply in the Zone Specific
Growth group box).
Clear clears the zone-specific growth settings attached to the zones selected in the Boundary Zones list.
List lists the zone-specific growth settings for the zones selected in the
Boundary Zones list in the console.
Plot displays (in the active graphics window) an illustration of the prism layers,
allowing you to preview the layer heights before actually creating the prisms.
The plot will show the layer heights for all selected boundary zones, and (if
different) the heights for the current settings in the panel.
Print reports the growth parameters, prism height for each layer, and total height
in the TGrid console. The report will show the data for all selected zones, and
(if different) the data for the current settings in the panel.
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Generating Prisms
Direction displays the controls for computing the growth directions for the nodes on
each layer of prisms.
Method lists the available methods for specifying the prism growth direction.
See Section 10.7: Direction Vectors for details about these methods.
Normal enables the computation of direction vectors normal to the boundary zones from which you are growing.
Uniform enables a uniform direction specification for all nodes on all prism
layers. When you select this method, you need to specify the direction
Vector.
TGrid will use this constant vector for all nodes on all prism layers, instead
of computing a new direction for each node on each layer. Therefore, this
option is most useful for creating straight-sided prism regions without any
curvature.
Flip Normals reverses the normal directions on the faces of the selected boundary
zone(s). The normal directions will determine the side of the boundary zone
on which prisms will be built.
Orient Normals orients contiguous faces (i.e., faces that touch each other) in a
selected zone so that their normals are all consistently pointing on the same
side of the zone (see Figure 7.13.1).
Max Angle Change specifies the maximum angle by which the normal direction
at a node can change during smoothing. See Sections 10.3.5 and 10.7 for
details about this parameter. This option is available only when the Normal
method is selected.
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10.10 The Prisms Panel
Vector specifies the uniform direction for all layers of prisms. You can either
enter values in the X, Y, Z fields, or click the Compute button to get the
average normal direction of the selected zone(s). This option is available only
when the Uniform method is selected.
Compute computes the average normal direction to the selected zone or zones
(i.e., the average of the unit normals of all the faces in the zones). This
direction is usually a good choice for the uniform direction, especially if the
zone is planar. This option is available only when the Uniform method is
selected.
!
If you use the Compute button to calculate the average normal direction,
do not change the sign of the displayed Vector. It is important for the
uniform direction vector to have the same sign as the normal direction for
the face zone.
Orthogonal Layers specifies the number of layers that should remain orthogonal
to the original boundary. For an orthogonal layer, TGrid will perform no edge
swapping or normal, edge, or node smoothing. See Section 10.3.5: Preserving Orthogonality for details. This option is available only when the Normal
method is selected and it is set to zero by default.
Improve contains the controls for various procedures used to improve the quality of
the prisms. These controls are not used if the Uniform direction method is selected.
Swapping and Smoothing contains controls for the edge swapping and smoothing,
and node smoothing.
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Swap Edges enables/disables edge swapping (see Section 10.9.1: Edge Swapping and Smoothing) to decrease the skewness of highly skewed faces. This
option is enabled by default.
Smooth Edges enables/disables edge smoothing (see Section 10.9.1: Edge
Swapping and Smoothing) to decrease the skewness of highly skewed faces.
This option is enabled by default.
Smooth Nodes enables/disables node smoothing (see Section 10.9.2: Node
Smoothing) to decrease the skewness of highly skewed faces. This option
is disabled by default.
Skewness specifies the face skewness above which edge swapping and smoothing are triggered. Only faces having skewness greater than this value are
evaluated for these operations. The default value is 0.7.
Warp contains options for improving face warp.
Improve allows you to improve face warp (see Section 10.9.3: Improving
Warp) during prism generation. This option is disabled by default.
Max Iter/Face specifies the maximum number of attempts for improving a
particular face.
Iterations specifies the number of iterations through the warp improvement
procedure.
Check Quality enables/disables the checking of face and cell quality after each
prism layer is created. When this option is enabled (the default setting), TGrid
will check the cell volume of every new cell, the face-handedness of every face
on every new cell, the skewness of all new cap faces (3D only), and the skewness
of all new cells (2D only).
If any new cell has zero or negative volume or any left-handed faces, or
if the skewness exceeds the specified Max. Allowable Skewness, prism layer
creation will be stopped. See Section 10.12: Negative Volumes/Left-Handed
Faces/High Skewness for details.
Max. Allowable Skewness specifies the maximum skewness allowed for a prism
cap face (in 3D) or a prism cell (in 2D). If the skewness exceeds the specified
value, TGrid will stop the meshing process and warn you that the skewness for
that layer is too high. You can then examine the skewed faces or cells, make
appropriate corrections, and recreate the prisms. See Section 10.12: Negative
Volumes/Left-Handed Faces/High Skewness for details.
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10.10 The Prisms Panel
Project contains controls for projection and retriangulation.
Retriangulate Adjacent Zones specifies whether or not the triangular face zones
adjacent to which outer nodes have been projected will be automatically retriangulated. This option is enabled by default. See Section 10.6: Retriangulation
for details about this procedure.
Max Adjacent Zone Angle sets the tolerance used to determine whether or not to
use an adjacent zone. If a zone shares outer nodes with any of the zones from
which the layers are being grown (the “base zones”), its angle with respect to
the growth direction is compared with the specified value. If the angle is less
than or equal to this value, then the zone will be used. See Section 10.6: Using
Adjacent Zones as the Sides of Prisms for details. The default is 45 degrees.
Side Feature Angle specifies the angle used for computing the feature normals.
Create creates the prisms using the settings specified in the panel.
Apply applies all current settings for prism growth, without creating the prisms. If
you wish to set the parameters in advance and return later to generate the prisms,
click Apply before closing the Prisms panel. There is no need to click Apply before
moving from one tab in the panel to another (e.g., from the Growth tab to the
Direct tab).
Note: Clicking Apply only applies the parameters set in the Prisms panel. When
setting prism parameters for use with the Auto Mesh option, click Apply in the
Zone Specific Growth group box for TGrid to retain the growth parameters on
specific zones in memory. The Prisms option in the Auto Mesh panel will be
visible only after applying zone-specific growth.
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Generating Prisms
Draw displays the boundary zone(s) selected in the Boundary Zones list. All current
settings in the Display Grid panel (see Section 14.1.3: The Display Grid Panel) will be
reflected in the resulting grid display. You may find it useful to enable the display
of normal vectors so that you can easily determine the normal direction(s) of the
selected boundary zone(s).
10.10.1
The Prisms Growth Options Panel
The Prisms Growth Options panel allows you to specify the parameters needed for detecting proximity/collision, retaining the first layer offset, and growing prisms individually
from multiple zones.
Controls
General Options contains additional options for prism growth.
Remove Invalid Layer allows you to retain the valid prism layers grown before
TGrid reports prism layer failure.
Grow Individually indicates whether individual prism cell zones and prism cap
face zones should be retained or merged with like zones. By default this
option is disabled, so a single zone of prism cells and a single zone of cap
faces will be created for each set of simultaneously grown layers. See Section 10.3.1: Growing Prisms Simultaneously from Multiple Zones for details.
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10.11 Text Interface for Generating Prisms
Ignore Invalid Normals allows you to ignore regions of invalid normals while creating prisms.
Proximity Options contains options for proximity detection.
Allow Shrinkage enables the shrinking of prism layers in areas of proximity to
avoid prism collision.
Keep First Layer Offsets allows you to retain the original first offset height while
scaling offset heights in case of intersecting prism layers.
Gap Factor controls the gap between the intersecting prisms layers with respect
to the cell size of the prisms.
Allow Ignore allows you to ignore prism growth parameters in areas of proximity
to avoid prism collision.
Max Shrink Factor determines the shrinkage of prism layers to avoid collision.
This option is available only when the Allow Ignore option is enabled.
Max Aspect Ratio specifies the maximum aspect ratio to determine the limit for
the shrinkage of prism layers. This option is available only when the Allow
Ignore option is disabled.
!
10.11
The value specified for Max Aspect Ratio is only used as a guideline for
limiting the shrinkage of the prism layers. The specified value may not
always be adhered to in the final mesh as the value may be relaxed during
the prism improvement operations such as smoothing, etc.
Text Interface for Generating Prisms
Text commands for generating prisms are listed below. Some of them allow additional
control that is not available in the Prisms panel.
/mesh/prism/create creates prism layers on the specified face zone(s) according to the
specified parameters.
/mesh/prism/controls/adjacent-zone/project-adjacent-angle sets the tolerance
used to determine whether or not to use an adjacent zone. If a zone shares outer
nodes with any of the zones from which the layers are being grown (the “base
zones”), its angle with respect to the growth direction is compared with this value.
If the angle is less than or equal to this value, then the zone will be used. See
Section 10.6: Using Adjacent Zones as the Sides of Prisms for details.
/mesh/prism/controls/adjacent-zone/project-converged sets the convergence criterion for iterative projection. This is non-dimensionalized by the offset height at
each local node.
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/mesh/prism/controls/adjacent-zone/project-iter sets the maximum number of
iterations to perform when projecting to multiple zones. Most projections converge
in only a few iterations. There is normally no need to change this value.
mesh/prism/controls/adjacent-zone/project? enables/disables projection of outer
nodes to adjacent zones.
mesh/prism/controls/adjacent-zone/retri-feature-angle allows you to specify the
feature angle that should be prevented while generating prisms.
mesh/prism/controls/adjacent-zone/retriangulate-adjacent? specifies whether or
not adjacent triangular face zones to which outer nodes have been projected will
be automatically retriangulated. This option is on by default.
/mesh/prism/controls/adjacent-zone/side-feature-align-angle specifies the angle used for aligning projected normals along a feature edge.
/mesh/prism/controls/adjacent-zone/side-feature-angle specifies the angle used
for computing the feature normals.
/mesh/prism/controls/adjacent-zone/side-topology-align-angle specifies the angle used for aligning projected normals along a particular feature edge based on the
topology. This is particularly useful when the side-feature-angle specified is
not sufficient to decide the feature edge to align the projected normals.
mesh/prism/controls/auto-separate-cells? toggles automatic movement of the cells
extruded from different face zones to different cell zones.
/mesh/prism/controls/check-quality? enables/disables the checking of volume, skewness, and handedness of each new cell and face.
/mesh/prism/controls/grow-individually? specifies whether TGrid should grow prisms
from multiple zones individually so that the individual prism cell zones and the individual cap face zones are retained.
/mesh/prism/controls/improve/check-allowable-skew? allows you to check the skewness of the prism cap for every layer.
/mesh/prism/controls/improve/check-size? enables the checking of cell size during
the generation of each prism layer. TGrid will report an error if zero-area prism
cells are generated and prism layer growth will be stopped.
When the check-size? option is disabled, the zero-area prism cells generated can
be removed during the improvement smoothing operations performed at the end of
the prism generation procedure.
/mesh/prism/controls/improve/edge-smooth? enables/disables local smoothing of nodes
of the longest edges of skewed faces.
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10.11 Text Interface for Generating Prisms
/mesh/prism/controls/improve/edge-smooth-angle specifies the maximum allowable
angle between the normals of adjacent cap faces for skewness-driven edge smoothing.
/mesh/prism/controls/improve/edge-swap? enables/disables edge swapping to decrease the skewness of highly skewed faces.
/mesh/prism/controls/improve/edge-swap-base-angle specifies the maximum allowable angle between a pair of base face normals for skewness-driven edge swapping.
/mesh/prism/controls/improve/edge-swap-cap-angle specifies the maximum allowable angle between a pair of cap face normals for skewness-driven edge swapping.
/mesh/prism/controls/improve/face-smooth? allows you to enable face-driven smoothing to improve skewness.
/mesh/prism/controls/improve/face-smooth-converged specifies the convergence criteria for cap face smoothing.
/mesh/prism/controls/improve/face-smooth-rings specifies the number of rings to
propagate skewness during smoothing of cap faces.
/mesh/prism/controls/improve/face-smooth-skew specifies the minimum skewness
to smooth cap faces.
/mesh/prism/improve/improve-warp? enables/disables improving of face warp during
prism generation. This option is disabled by default.
/mesh/prism/controls/improve/left-hand-check specifies checking for left-handedness
of faces. A value of 0 implies face handedness will not be checked, 1 implies only
cap faces will be checked, while 2 implies faces of all cells in current layer will be
checked.
/mesh/prism/controls/improve/max-allowable-skew specifies the maximum allowable skewness for cap faces after smoothing. Prism layer growth will be stopped if
any cap face has skewness greater the specified value.
/mesh/prism/controls/improve/node-smooth? allows you to enable node-driven smoothing to improve skewness.
/mesh/prism/controls/improve/node-smooth-angle refers to the maximum deviation of a node’s sharpest angle (i.e., the most acute angle between adjacent faces
that use the node) from 180 degrees. The node will be smoothed only if its sharpest
angle falls within this range. For example, if the specified value is 45 degrees, nodes
with sharpest angles between 135 and 225 degrees can be smoothed.
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/mesh/prism/controls/improve/node-smooth-converged sets the convergence criterion for node smoothing. If the node positions are changing by less than this value,
smoothing iterations will stop.
/mesh/prism/controls/improve/node-smooth-iter specifies the maximum number of
node smoothing iterations to be performed for the nodes on each layer. These
iterations will be performed until the convergence criterion is reached.
/mesh/prism/controls/improve/node-smooth-local? allows you to enable node smoothing to converge locally. This is useful for large geometries.
/mesh/prism/controls/improve/node-smooth-rings controls the locality of node smoothing by setting the number of rings around each node to be smoothed.
• If zero, only a node itself is smoothed. If one, the node and all of its neighbors
are smoothed.
• If two, the neighbors of the neighbors are also smoothed, and so on.
/mesh/prism/controls/improve/shrink-left-handed-cap? allows you to enable shrinking of prism layers to get rid of left handed faces.
/mesh/prism/controls/improve/swap-smooth-skew specifies the skewness threshold
for edge swapping and edge and node smoothing. The faces with skewness greater
than or equal to the specified value will be swapped and/or smoothed.
/mesh/prism/controls/merge-ignored-threads? allows you to automatically merge
all ignored zones related to a base thread into a single thread. This option is
enabled by default. When this option is disabled, TGrid will generate more than
one thread per base thread.
mesh/prism/normal/bisect-angle is required for growing prisms out of sharp interior
corners. When the value of this angle is set, the normals are automatically projected
onto the plane bisecting the angle between faces having an interior angle less than
this angle.
/mesh/prism/normal/converge-locally? specifies whether or not the normal smoothing at each node is frozen once convergence is satisfied at that node. If not, all
normals are continuously smoothed until all of them have converged.
/mesh/prism/controls/normal/direction-method specifies whether the prism layers
should be grown normal to surfaces or along a specified direction vector.
/mesh/prism/controls/normal/ignore-invalid-normals? allows you to ignore nodes
which have poor normals.
/mesh/prism/controls/normal/intersect-detect? enables the adjustment of normals
to avoid their intersection.
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10.11 Text Interface for Generating Prisms
/mesh/prism/controls/normal/intersect-detect-angle specifies the angle based on
which normal intersection is determined. The normal intersection is determined in
cases when the feature angle of the manifold of a node is less than the value specified.
/mesh/prism/controls/normal/max-angle-change specifies the maximum angle by which
the normal direction at a node can change during smoothing.
mesh/prism/controls/normal/normal-method specifies the method to use for normal
direction computation (see Section 10.7: Direction Vectors).
acute-bisection is a variation of that proposed by Kallinderis et al. [?],[?][?, ?].
The faces surrounding a node are analyzed to find those whose planes form
the most acute angle. The resulting normal lies on the plane bisecting those
two planes.
This method is computationally more expensive than surface averaging, but is
less robust at singular points where convex edges meet smooth surfaces. For
example, if a box is sitting on the table, such a point would be where one of
the box’s corners meets the table top.
face-average computes the normal at a node by averaging the normals of the
surrounding faces. This is the only method available in 2D.
hybrid-normal computes the normal by all the methods available and uses the
best quality normal obtained. This is the default method in TGrid.
minimized-angle is a variation of that proposed by Pirzadeh [?],[?]. An initial
normal at a node is determined by averaging the normals of the surrounding
faces (the face-average method). Iterations are then performed to minimize
the largest angle between the node normal and the normals of the surrounding
faces.
This method is a computationally more expensive than surface averaging, and
can produce slightly better normals when the uniform offset method is used
and the surface mesh does not contain sharp edges. When the minimumheight offset method is used, this direction method may introduce spikes and
pits in the advancing layer surfaces.
surface-average is similar to face-average, but handles sharp edges better.
This is the default method in 3D.
/mesh/prism/controls/normal/orthogonal-layers specifies the number of layers to
preserve orthogonality. All smoothing is deferred until after these layers have been
generated.
/mesh/prism/normal-smooth? enables or disables smoothing of normal direction vectors.
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mesh/prism/normal-smooth-converged sets the convergence criterion (in degrees) for
normal smoothing. If the normal directions are changing by less than this value,
smoothing iterations will stop.
/mesh/prism/normal-smooth-iter specifies the maximum number of normal smoothing iterations to be performed for the normal vectors on each layer. These iterations
will be performed until the convergence criterion is reached.
/mesh/prism/controls/offset/smooth? enables/disables offset distance smoothing.
/mesh/prism/controls/offset/smooth-converged sets the convergence criterion for
offset smoothing. If the offset heights change by less than this value, smoothing
iterations will stop.
/mesh/prism/controls/offset/smooth-iter sets the maximum number of offset smoothing iterations to be performed. These iterations will be performed until the convergence criterion is reached.
/mesh/prism/controls/proximity/allow-ignore? allows you to ignore nodes where
specified maximum shrink factor cannot be maintained.
/mesh/prism/controls/proximity/allow-shrinkage? allows you to enable shrinkage
while growing prism layers.
/mesh/prism/controls/proximity/gap-factor specifies the gap between prism layers
in the proximity region.
/mesh/prism/controls/proximity/keep-first-layer-offsets? allows you to retain
first layer offsets while performing proximity detection.
/mesh/prism/controls/proximity/max-aspect-ratio specifies the minimum offset to
avoid degenerate cells. This option is available only when the allow-ignore?
option is disabled.
/mesh/prism/controls/proximity/max-shrink-factor specifies the shrink factor determining the maximum shrinkage of the prism layers. This option is available only
when the allow-ignore? option is enabled.
/mesh/prism/controls/proximity/smoothing-rate specifies the rate at which shrinkage is propagated in lateral direction.
/mesh/prism/controls/remove-invalid-layer? removes the last prism layer if it fails
in the quality check.
/mesh/prism/controls/zone-specific-growth/apply-growth applies the zone-specific
growth parameters specified.
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10.12 Prism Meshing Problems
/mesh/prism/controls/zone-specific-growth/clear-growth clears the zone-specific
growth specified.
/mesh/prism/controls/zone-specific-growth/list-growth lists the zone-specific growth
parameters specified for individual zones in the console.
/mesh/prism/improve/improve-prism-cells smoothes cells by considering rings of
cells around the prism cells.
/mesh/prism/improve/smooth-brute-force? forcibly smooth cells if cell skewness is
still high after regular smoothing.
/mesh/prism/improve/smooth-cell-rings specifies the number of cell rings to be considered around the skewed cells (to be used by improve-prism-cells).
/mesh/prism/improve/smooth-prism-cells specifies optimization based smoothing of
prism cells.
/mesh/prism/improve/smooth-sliver-skew specifies the skewness above which prism
cells will be smoothed.
/mesh/prism/list-parameters lists all prism mesh parameters in the console.
/mesh/prism/reset-parameters resets the prism parameters to their defaults.
i
If you read in a mesh file created in a previous version of TGrid, you can
reset all the prism parameters using this command before proceeding with
setting the prism parameters.
/mesh/revolve-face-zone generates prisms by revolving a specified face zone through
a specified angle about a specified rotation origin and axis to produce a polar mesh.
10.12
Prism Meshing Problems
This section discusses a number of common problems that you may encounter when generating prismatic meshes. A appropriate solution is also recommended for each problem.
If the prism generation fails or is unsatisfactory, read in the mesh you saved before starting the prism generation (in step 6 of Section 10.2: Procedure for Generating Prisms)
and repeat the process, incorporating the appropriate corrections.
The most common prism meshing problems are:
• Orientation
• Retriangulation failures
• Too many or too few nodes, or unknown face combinations
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Generating Prisms
• Negative volumes, left-handed faces, or high skewness
• Growing too far
• Large jumps in prism height at the edges of layers
Orientation
If the faces of the boundary zone from which you are building prisms are not all oriented in the same direction (Figure 7.13.1), TGrid will stop the prism generation process
immediately and will alert you that it has reoriented the faces.
Solution: In this case, do the following:
1. Check the normal direction vectors on the boundary zone, to ensure that they have
not been oriented to face in the wrong direction.
2. Follow the instructions in step 4 in Section 10.2: Procedure for Generating Prisms
to check and, if necessary, correct (flip) the normal direction.
3. Click Create to restart the prism generation process.
In this case, there is no need to reread the mesh because TGrid stops before it
actually creates any prism layers.
Retriangulation Failures
If nodes, where adjacent zones meet the zones (from which prisms are growing) are
duplicated, TGrid will be unaware that the zones are connected. It will ignore such zones
when considering nodes for projection, and hence retriangulation is likely to fail.
Solution: To verify this problem check the messages printed before the first prism layer.
It should contain a list of all the zones connected to the zones from which you are growing
the prisms.
1. Make sure there are no free nodes in the surface mesh before growing any prisms.
2. Use the Count Free Nodes button in the Merge Boundary Nodes panel (see Section 7.1.2: The Merge Boundary Nodes Panel) to check for free nodes.
3. Turn on the Free option in the Faces section of the Display Grid panel, to see where
the free nodes are located.
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10.12 Prism Meshing Problems
Too Many/Few Nodes or Unknown Face Combinations
If you receive the following type of messages, then you are most likely growing prisms
into existing cells.
Warning: wedge cell c887 has too many nodes
Warning: wedge cell c1928 has too few nodes
Warning: base_mask = 7 (0x7), unknown face combinations
Either you have already grown prisms from the selected zones, or you are growing them
in the wrong direction into cells on the other sides of the selected zones. In the latter
case, click the Flip Normals button in the Direct section of the Prisms panel before growing
the layers. See step 4 in Section 10.2: Procedure for Generating Prisms.
Negative Volumes/Left-Handed Faces/High Skewness
TGrid will automatically stop the prism layer creation process if it detects negative cell
volumes, left-handed faces, or high skewness.
Left-handed faces are faces that have collapsed into their cells. You can view them by
turning on the Left Handed option in the Faces section of the Display Grid panel. Very high
skewness occurs when the value of skewness is greater than the specified Max. Allowable
Skewness in the Improve section of the Prisms panel). These problems can occur where
prism layer fronts are advancing too quickly in areas of high curvature.
For example, the first layer height may be greater than the minimum edge length of your
original surface mesh. You should compare the First Height with the results of clicking
the Edge Size Limits button in the Growth section of the Prisms panel. The First Height
should usually be smaller than the minimum edge size.
Solution: If the First Height is reasonable but TGrid is unable to successfully generate
your requested Total Height, try one of the following solutions:
• Reduce the First Height or the parameter used for the growth Method (i.e., Slope,
Rate, or Exponent), and increase the Number of Layers. Extra layers allow smoothing
to compensate better for sharp edges and corners.
• If you have specified a nonzero value for Orthogonal Layers (in the Direct section of
the Prisms panel), change it to zero. Increasing orthogonality can reduce robustness.
• If you have reduced the Max. Angle Change (in the Direct section of the Prisms
panel) from its default of 70 degrees to improve orthogonality, reset it to 70.
• If you have disabled edge swapping or normal, offset, or edge smoothing, turn them
back on.
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Generating Prisms
• If you are using the minimum-height offset method (enabled with the
mesh/controls/prism/offset-method text command), switch back to the uniform method.
• Lower the Skewness for Swapping and Smoothing in the Improve section of the Prisms
panel.
• Increase the number of Layers in the Improve section of the Prisms panel if it is
smaller than the number of layers being grown.
• Enable Smooth Nodes in the Improve section of the Prisms panel. You can also
increase the number of smoothing rings, using the following TUI commands:
mesh/controls/prism/node-smooth-rings
• If you are growing simultaneously from multiple zones, use zone-specific growth
controls. Use smaller initial heights and/or growth rates for zones that are having
problems.
Growing Too Far
The problem here is growing too many layers. Ideally, to provide for a smooth transition
to the nearly-equilateral tetrahedra, the volume of the tetrahedra should be the local
growth rate times the volume of the last layer prism cells.
Solution: To ensure this does not happen, verify that the prism parameters satisfy the
above condition.
Large Jumps in Prism Height
If the prisms use quadrilateral faces of adjacent zones, and the node spacings on these
faces are very different from the layer heights, the prism heights jump at the outer edges.
Solution: To fix this problem, replace the adjacent quadrilateral face zones with triangular face zones, using the boundary/create-tri-surface text command. When you
reattempt the prism generation, TGrid will project to and retriangulate the zone.
Since TGrid projects the outer nodes of the prisms to the adjacent boundary zone, and
discards the original nodes on that portion of the zone, the different node spacing on the
adjacent zone will not affect the prism heights at the outer edges.
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